From Wikipedia http://en.wikipedia.org/wiki/Hillary_Rodham_Clinton :
...volunteered for Republican candidate Barry Goldwater in the U.S. presidential election of 1964.[13]
College
In 1965, Rodham enrolled in Wellesley College, where she majored in political science.[15] She served as president of the Wellesley Young Republicans organization during her freshman year.[16][17] However, due to her evolving views regarding the American Civil Rights Movement and the Vietnam War, she stepped down from that position;[16] she characterized her own nature as that of “a mind conservative and a heart liberal.”[18] ... and became a supporter of the anti-war presidential nomination campaign of Democrat Eugene McCarthy.[...
She attended the “Wellesley in Washington” summer program at the urging of Professor Alan Schechter, who assigned Rodham to intern at the House Republican Conference so she could better understand her changing political views.[20] Rodham was invited by Representative Charles Goodell, a moderate New York Republican, to help Governor Nelson Rockefeller’s late-entry campaign for the Republican nomination.[20]
Rodham attended the 1968 Republican National Convention in Miami, where she decided to leave the Republican Party for good; she was upset over how Richard Nixon’s campaign had portrayed Rockefeller and what Rodham perceived as the “veiled” racist messages of the convention.[20]
I just had to go look at footnote "20" in Wikipedia to see what Nixon said that was so "racist".
Turns out it's a cite of Clinton's own quote (long after 1968) on her "perception" of the Republican convention:
At the party’s convention in Miami, she met Frank Sinatra, shared an elevator with John Wayne and decided to leave the Republican Party for good. “She was particularly furious at how she felt Rockefeller had been trashed by the Nixon people,” Mr. Schechter said.
“I’m done with this, absolutely,” Mrs. Clinton recalled thinking upon hearing Mr. Nixon’s acceptance speech. She characterized the Republicanism of her youth as one of fiscal conservatism and social moderation, and at odds with what she viewed as the intolerance of Miami.
“All of a sudden you get all these veiled messages, frankly, that were racist,” Mrs. Clinton said of the convention. “I may not have been able to explain it, but I could feel it.”
So even back then a Clinton was parsing her words and tap dancing. This is, of course, if you believe this was her mindset 40 years ago and not just made-up around the year 2000.